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In this lesson, you will study how to use operations to solve problems involving monomials, binomials, polynomials, and algebraic fractions.
You can add monomials if they are like terms. Like terms have the same variable raised to the same
exponent. For example, 
. Terms such as 4x and 5y cannot be added because they have different variables. Terms such as 4x and 
cannot be added either; even though they have the same variable, it is raised to different powers.
These same rules apply to subtraction of monomials.
Which choice shows the correct simplification of 
?
The correct answer is D. To simplify the polynomial, combine the like terms: 6xy and 10xy are like terms, so 
. Because 16xy , 3x , and 9y are not like terms, they cannot be combined. The polynomial simplifies to 
.
Monomials can be multiplied regardless of their variables and exponents. Examples: 
and
. To do so, first multiply the numerical coefficients. Then, if variables have the same base, multiply them together by adding the exponents. Division of monomials is done the same way, except the exponents are subtracted.
Which choice shows the correct result of multiplying 
?
The correct answer is A. To solve, multiply the coefficients, multiply the variables, and then combine.
To add binomials, combine like terms. For example, 
. Subtraction of binomials is done the same way.
Which choice shows the correct result of adding 
?
The correct answer is A. Combine the like terms. Because 4x and 3x are like terms, add them together to get 7x. 7x , 2y , and 7 are not like terms so the final polynomial is 
.
One way to multiply binomials is to use the FOIL method. FOIL stands for “first, outside, inside, and last.” For example, 
can be multiplied by the FOIL method.
The F in FOIL tells you to multiply the first term in each binomial.
The O in FOIL tells you to multiply the two outside terms.
The I in FOIL tells you to multiply the two inside terms.
Then add these terms together by combining like terms.
Which choice shows the correct result of multiplying 
?
The correct answer is C. Use the FOIL method to solve.
To multiply polynomials, multiply each term in the first polynomial by each term in the second polynomial, and then combine like terms. For example,
Which choice shows the correct result of multiplying 
?
The correct answer is B. Multiply each term in the first polynomial by each term in the second polynomial, and then combine like terms.
To simplify an algebraic fraction, factor both the numerator and denominator and then cross out like terms. For example,
Which choice shows the correct simplification of 
?
The correct answer is A. Factor the numerator and denominator and then simplify.
